# Solving with logs

1. May 19, 2013

### Mermaid4220

1. The problem statement, all variables and given/known data

log base u (x)=2.26
log base u (y)=2.84
log base u (z)=4.38
find ;
x^2*y^5/z^4

2. Relevant equations

3. The attempt at a solution
I have tried many things raising each of the numbers to their exponents and dividing, using laws of the exponents it state we have to have the exact answer with no instructions as to what decimal point or just the formula or what...can anyone help either get me started or understand what I am supposed to do?

2. May 19, 2013

### verty

I think what is meant is, be as exact as you can be and simplify that formula as much as possible. At the moment it has 3 unknowns, can you do something about that?

3. May 19, 2013

### Mermaid4220

I inserted the numbers x=2.26 and so forth and tried many different ways and all the answers i got were not excepted....:( its probably an easy thing as it is in the first part of the homework but it seems I make the easiest thing hard for some reason :)

4. May 19, 2013

### CAF123

I would first solve the equations for x,y and z separately. Then label 2.6, 2.84 and 4.38 by a,b,c (so that in the end you get an exponent u^f, where f is entirely in terms of a,b,c - this avoids mid calculation rounding errors) and substitute x,y,z into the expression you need to find the value of. I think this is what you were trying but couldn't get any further?

5. May 19, 2013

### LCKurtz

Call the quantity $w=\frac{x^2y^5}{z^4}$. What is $\log_u(w)$? Then what is $w$? The answer will depend on $u$.

6. May 19, 2013

### Mermaid4220

Its actually called u= not w= does that make a difference?

7. May 19, 2013

### LCKurtz

????

You are using u as the base of your logs aren't you? I was just giving a name to your expression.

8. May 19, 2013

### SammyS

Staff Emeritus
It's my experience that such a problem would likely to ask you
to find :
$\displaystyle \log_{\,u}\left( \frac{x^2y^5}{z^4}\right)\ .$​

Finding this quantity first would help, even if it's not asked for.

9. May 19, 2013

### Mermaid4220

That is exactly what they want and I found the quantity and tried several different ways of doing it but the program Wiley will not accept the answers :( I will get help tomorrow at school thanks anyways guys :)